Question: Simplify the following expression: $n = \dfrac{-5r^2 + 35r - 30}{r - 6} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ n =\dfrac{-5(r^2 - 7r + 6)}{r - 6} $ Then we factor the remaining polynomial: $r^2 {-7}r + {6} $ ${-6} {-1} = {-7}$ ${-6} \times {-1} = {6}$ $ (r {-6}) (r {-1}) $ This gives us a factored expression: $\dfrac{-5(r {-6}) (r {-1})}{r - 6}$ We can divide the numerator and denominator by $(r + 6)$ on condition that $r \neq 6$ Therefore $n = -5(r - 1); r \neq 6$